Physics Cosmology Depth From Rs

Cosmology Depth

Cosmology depth, in the Recognition Science framework, is the number of distinct large-scale eras a universe passes through. The framework's machine-checked library of formal theorems defines exactly five: inflation, radiation-dominated, matter-dominated, dark energy-dominated, and a future de Sitter phase. This matches the standard sequence in conventional cosmology, where the universe inflates, then cools through radiation and matter eras, then accelerates under dark energy into an eternal exponential expansion.

The classical picture is well established. Inflation, proposed by Alan Guth in 1980, explains the universe's flatness and uniformity. Radiation domination followed, when photons and neutrinos governed the expansion rate. Matter domination took over as the universe cooled, allowing galaxies to form. Dark energy, discovered through supernova observations in 1998, then began accelerating the expansion, leading toward a de Sitter phase of exponential growth. Each epoch has a distinct equation of state and a distinct effect on the scale factor of the universe.

In Recognition Science, the framework models each epoch as a different cost regime in its recognition field. The recognition field, a field whose local value records the cost of registering an event, behaves differently in each era. Inflation ends when the cost J tends to zero at reheating, the moment the inflaton field decays into particles. Radiation domination has a thermal cost. Dark energy domination locks the cost at a constant value J(φ), which the framework derives in its own development as Λ_RS = 8φ⁵/45, approximately 1.91 in its native units.

The framework's contribution is formal, not observational. Its library proves a theorem, cosmologicalEpochCount, that the number of epochs is exactly five. This is a statement about the framework's own definitions, not a new measurement of the universe. The theorem is checked by the machine with zero unproven assumptions, meaning the count follows from the framework's axioms alone. The physical identification of each epoch with a cost regime is a modeling choice, not a derived law.

What this establishes in plain language is a structural parallel: the five eras astronomers observe correspond, in the framework, to five distinct cost regimes of a single underlying field. The framework does not predict the existence of dark energy or the order of the epochs; it takes the standard sequence as given and shows how its own machinery can label each era. The number five is not derived from first principles here; it is a definitional count of the epoch types the framework recognizes.

theorem cosmologicalEpochCount : Fintype.card CosmologicalEpoch = 5 := by decide

inductive CosmologicalEpoch where
  | inflation | radiationDominated | matterDominated | darkEnergyDominated | futureDeSitter
  deriving DecidableEq, Repr, BEq, Fintype

inductive CosmologicalEpoch where
  | inflation | radiationDominated | matterDominated | darkEnergyDominated | futureDeSitter
  deriving DecidableEq, Repr, BEq, Fintype

What this page does not claim

The framework does not predict the existence or order of the five epochs from first principles. The value Λ_RS = 8φ⁵/45 is derived in the framework's own development, not yet checked by the machine. The theorem that the count is five is a definitional result, not an empirical discovery.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Physics/CosmologyDepthFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: